Hong-Ou-Mandel Interference with a Single Atom

Abstract

The Hong-Ou-Mandel (HOM) effect is widely regarded as the quintessential quantum interference phenomenon in optics. In this work we examine how nonlinearity can smear statistical photon bunching in the HOM interferometer. We model both the nonlinearity and a balanced beam splitter with a single two-level system and calculate a finite probability of anti-bunching arising in this geometry. We thus argue that the presence of such nonlinearity would reduce the visibility in the standard HOM setup, offering some explanation for the diminution of the HOM visibility observed in many experiments. We use the same model to show that the nonlinearity affects a resonant two-photon propagation through a two-level impurity in a waveguide due to a "weak photon blockade" caused by the impossibility of double-occupancy and argue that this effect might be stronger for multi-photon propagation.

Figure 1. Traditional Hong-Ou-Mandel interference scheme.

Two identical photons arriving simultaneously at a balanced, broadband beam splitter (BS) will be conveyed along only one of the possible outgoing channels—and so, in contrast to the general case, no coincidence counts will be accumulated.

Figure 2. Two additional geometries described by the model of Eq. (1):

(a) a single atom (TLS) embedded in a 1D photonic crystal waveguide leads to reflection of resonant photons in the channel (off-resonant photons are freely transmitted); (b) an interstitial TLS provides a resonant link between two waveguide channels.

Figure 3. The anti-bunching probability in the HOM geometry.

Neglecting the nonlinearity (independent scattering), it goes to 0 with (the monochromatic limit), which corresponds to the balanced beam splitter. The nonlinearity makes the probability of anti-bunching finite for any value of Γ (the solid line describes the exact numerical solution); the analytic asymptotics (the strong-coupling—monochromatic—limit) practically coincides with the exact solution for .

Figure 4. Weak photon blockade.

Here δP_res is the nonlinearity-induced anti-bunching probability in the resonance geometry of Fig. 2(b), i.e. the probability of reflecting one out of two photons, as a function of their relative delay Δ = στ. The inset shows a non-monotonic behaviour of the total anti-bunching probability due to a trivial off-resonance reflection at smaller Γ.